II— III] 



Introduction 



xix 



Therefore by formula (i) p. xiii : 



*, = -398,6233 --58 [1793] + -^! — [397] , 



= -398,6233] 



- 1040 > = -398,5241. 

 + 48j 



Or, we might proceed as follows: for the Poll-men £(1 - a) - -4817, hence 

 a = -0366. But from Table III, p. 9, which gives z for a : 



« = -03, z = -398,6603 



a = 04, z = -398,4408 



= -66, A,= -2194 



A,= -627. 

 Hence by formula (i) : 



■RR y -«J4 



*, = -398,6603 - -66 [2194] + — ~- [627] 



- -398,6603' 



- 1448 [• =-398,5225. 



+ 70 



We conclude therefore that z would be correct to five figures with second differ- 

 ences, and that for four figures, first differences from either Table II or Table III 

 will suffice. 



If we use formula (ii) p. xiii — Everitt's formula — we find from Table II: 

 4 = 398,6233 - -58 [1793] + *§ *«" [397] + ^ * fl 8236 [398] 



6 



= -398,6233 



-1040 



+ 13 



+ 5 



and from Table III : 



•398,5211, 



*, = -398,6603 - -66 [2194] + I^IL**** [62 7] + 34 * ~ 8844 [627] 



= 398,6603 

 -1448 



+ 

 + 



37 

 31 ) 



•398,5223. 



Working with formula (iii), Table II gives us z 1 m 398,5242 and Table III 

 z x = -398,5225 with second differences. We shall not therefore without higher 

 differences get from any of our formulae closer than -398,522 with a possible error 



c2 



